2nd Semester 2023/24: Classification Aggregation and the Group Identification Problem

Federico Fioravanti

Consider a set of neural networks that has to classify different images into different categories of animals, or a group of managers that has to assign different workers to different tasks. How can these classifications or assignations be done? These are particular situations of the general case where a set of n agents has to classify a set of m objects into p different categories, which is known as a classification aggregation problem.

A particular setting of this problem is when the set of individuals has to classify themselves into different categories (or groups), based on their own opinions, and it is known as the Group Identification Problem.

These topics lie in the larger area of computational social choice which deals with the aggregation of individual opinions into a collective outcome.  Research in the field is done by mathematicians, economists, philosophers, and computer scientists alike.

This project aims to give students an overview of these topics and see under what conditions the aggregations of classifications can be done.


The first week will consist of a series of presentations given by the instructor on some selected topics (described above).
During the second week, the students should select a paper from the literature to give a short presentation, while also starting to think on a research topic of their own (individually or in group). The presentation will be given on the Monday of the third week, while the rest of the course will be used to develop the research topic, which will be documented and handed in at the end of the fourth week. The sizes of the groups will be determined according to the number of students.


Prior knowledge of social choice theory will make it easier for the students but is not required (as the basics are going to be discussed during the first week). Good mathematical maturity is needed.


The students will be assessed based on two things: the oral presentation and the final paper. Attendance at the other student’s presentations is mandatory.


Handbook of Computational Social Choice, Cambridge University Press, 2016.

Handbook of Social Choice and Welfare, Elsevier 2002

Kasher, Asa, and Ariel Rubinstein. "On the question" who is a J?": A social choice approach." Logique et Analyse (1997): 385-395. 

Maniquet, François, and Philippe Mongin. "A theorem on aggregating classifications." Mathematical Social Sciences 79 (2016): 6-10.